Problem: Solve for $x$ and $y$ using elimination. ${2x-6y = -12}$ ${5x+3y = 60}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $2$ ${2x-6y = -12}$ $10x+6y = 120$ Add the top and bottom equations together. $12x = 108$ $\dfrac{12x}{{12}} = \dfrac{108}{{12}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {2x-6y = -12}\thinspace$ to find $y$ ${2}{(9)}{ - 6y = -12}$ $18-6y = -12$ $18{-18} - 6y = -12{-18}$ $-6y = -30$ $\dfrac{-6y}{{-6}} = \dfrac{-30}{{-6}}$ ${y = 5}$ You can also plug ${x = 9}$ into $\thinspace {5x+3y = 60}\thinspace$ and get the same answer for $y$ : ${5}{(9)}{ + 3y = 60}$ ${y = 5}$